In-Person Talk 

Given a surface diffeomorphism representing a pseudo-Anosov mapping class, the number of fixed points of its iterations grows exponentially. This property actually distinguishes pseudo-Anosov classes from other ones. For a pair of non-contractible simple curves on a surface with geometric intersection number at least 3, the composition of their Dehn twists defines a pseudo-Anosov mapping class according to Thurston. I will explain how to understand this fact using symplectic geometry and discuss its generalization in higher dimensions using the Picard-Lefschetz theory.